Lectures related to Networked Control Systems: Convergence Rate and Digraphs

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Covers the concept of networks, graphs, subgraphs, directed graphs, and indegree in network theory.

Covers bipartite and n-partite graphs, including complete graph definitions and examples.

Covers edge elimination and orientation in graphs, including first order tests and logical orientation.

Explores handling network data, including types of graphs, real-world network properties, and node importance measurement.

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Explores time-varying consensus algorithms in networked control systems and the Laplacian matrix's role in achieving average consensus.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Covers the basics and applications of graph coloring, including balancing vectors and achieving perfect fairness.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Explores Ramsey theory, alterations, colorings in graphs, monochromatic matchings, and the significance of large cliques.

Explores the role of graphs in deep learning, focusing on their structure, applications, and techniques for processing graph data.

Explores Laplacian operators on graphs and the model of DC microgrids.

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.